Recent Advances in Dakota UQ

Transcription

1 SAND C Recent Advances in Dakota UQ Brian M. Adams Optimization and Uncertainty Quantification Patricia D. Hough Quantitative Modeling and Analysis ASME V&V Symposium 2016 May 18 20, 2016 Las Vegas, NV Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy s National Nuclear Security Administration under contract DE-AC04-94AL85000.

2 DAKOTA GOALS AND CAPABILITIES 2

3 SNL Mission: Advanced Science and Engineering for National Security Nuclear Weapons Defense Systems and Assessments Energy and Climate International, Homeland, and Nuclear Security Strong research foundations span many disciplines Dakota Mission: To serve Sandia s mission through state-of-the-art research and robust, usable software for optimization and uncertainty quantification. Dakota Team: has balanced strengths in algorithm research, software design and development, and application deployment and support 3

4 Dakota: Algorithms for Design Exploration and Uncertainty Quantification Suite of iterative mathematical and statistical methods that interface to computational models Makes sophisticated parametric exploration of black-box simulations practical for a computational design-analyze-test cycle: Sensitivity Analysis Uncertainty Quantification Design Optimization Model Calibration input parameters simulation model Goal: provide scientists and engineers (analysts, designers, decision makers) richer perspective on model predictions response QOIs 4

5 Diverse Simulations Across Scales Systems of systems analysis: multi-scale, multi-phenomenon Shock loading of polymer foam: molecular dynamics Joint mechanics: system-level FEA for component assessment Micro-electro-mechanical systems (MEMS): quasi-static nonlinear elasticity, process modeling Electrical circuits: networks, PDEs, differential algebraic equations (DAEs), E&M Emergencies: weather, logistics, economics, human behavior 5

6 Supports Overall Simulation Workflow Including Verification and Validation Enables quantification of margins and uncertainty (QMU) and design with simulations; analogous to experiment-based QMU and physical design/test verification uncertainty-aware validation sensitivity analysis to down-select design of computer experiments calibration / comparison with data ASME Guide for V&V in Computational Solid Mechanics 6

7 Many Methods in One Tool Sensitivity Analysis Designs: MC/LHS, DACE, sparse grid, one-at-a-time Analysis: correlations, scatter, Morris effects, Sobol indices Optimization Gradient-based local Derivative-free local Global/heuristics Surrogate-based, multi-fidelity Uncertainty Quantification MC/LHS/Adaptive sampling Local/global reliability Stochastic expansions Epistemic methods Multi-fidelity/multi-level Calibration Tailored gradient-based Use any optimizer Bayesian inference One flexible simulation interface, many methods: once interface created, apply appropriate algorithm depending on question at hand Scalable parallel computing from desktop to HPC 7

8 Engineering Needs Drive Dakota R&D Advanced approaches help you solve practical problems, including with nonsmooth, discontinuous, or multi-modal responses: Characterize parameter uncertainty Bayesian calibration Hybrid analysis mix methods, surrogates, and models Mixed uncertainty characterizations epistemic and mixed uncertainty forms and propagation Costly simulations surrogate-based, multi-fidelity optimization and UQ Build in safety or robustness combined deterministic/ probabilistic methods min s.t. 8

9 Dakota History and Resources Genesis: 1994 optimization LDRD Modern software quality and development practices Released every May 15 and Nov 15 Established support process for SNL, partners, and beyond Mike Eldred, Founder Lab mission-driven algorithm R&D deployed in production software Extensive website: documentation, training materials, downloads Open source facilitates external collaboration; widely downloaded 9

10 RECENT AND FUTURE DAKOTA DEVELOPMENT 10

11 Inference: Bayesian Calibration Goal: Obtain statistical characterization of parameters consistent with data MCMC with DRAM and DREAM; emerging non-mcmc-based approaches Research (Eldred) in adaptive, surrogate-based inference; use derivatives to precondition proposal covariance to increase acceptance rates Usability: support all variable types, chain postprocessing, statistics, credible/prediction intervals, KDE-smoothed posteriors, mutual information Experiment data and covariance handling Next: model discrepancy, iterative DOE Collaborations: UT Austin, LANL, NC State MLE MAP 11

12 Core UQ Method Improvements Robust, scalable, usable UQ methods Sampling New: Incremental and batch sampling, Wilks criterion-based sample size, D-optimal designs based on Leja sequences Improved adaptive importance sampling New recursive k-d darts (RKD) sampling Generalized multi-level Monte Carlo Geometric to treat multiple discretization levels (ML) Control variate to treat multiple hierarchical model forms (MF) D-optimal design for discrete variables Stochastic Expansions Non-intrusive polynomial chaos, stochastic collocation, various integration schemes, adaptivity Adaptive basis selection for compressed sensing Import/export of expansions and approximate evaluations 12

13 Active Subspace Identification Goal: Scale sensitivity analysis, UQ, optimization, and surrogates by finding an input parameter subspace Many algorithm, correctness, and usability improvements (Monschke) Several subspace identification criteria Can perform UQ with sampling, PCE, and reliability methods; others and more variables types coming Next: derivative-free approaches (with NC State) xx = WW 11 yy + WW 22 zz Piecewise Local Surrogates Build on meshing research: maximum Poisson disk sampling, approximate Voronoi cell identification, recursive k-d darts Construct global (piecewise local) surrogates with discontinuity detection, without explicit Constantine, meshing

14 Random Field Modeling Goal: perform UQ with field-valued (time- or spacevarying) input uncertainties f(t, x), e.g., boundary conditions Generate realizations of f(t; u): either sample the field-generating model or use offline data Approximate uncertainty in f(t; u), e.g., by a Karhunen Loève expansion with normal coefficients ω ff tt, ωω = μμ ff tt + cc ii ωω φφ ii Propagate: perform UQ over ω, generating realizations of the approximate field ff tt, ωω and propagate through the field-accepting model PP ii=1 tt uncertain input parameters u fieldgenerating model field-valued outputs f(t,x;u) become inputs fieldaccepting model ultimate quantities of interest 14

15 Promote User and Development Community Engagement Web resources: Interactive user forums Capability maturity ratings and test linkage Community repository of code, examples, scripts Training materials: presentations, videos, exercises New graphical user interface for Dakota analysis Improved modularity so users can extend, contribute components, e.g., Surrogate model module with Python bindings More usable simulation interfacing that encourages best practices Communicate development practices to encourage contribution, e.g., principles, code standards, easier build/test on new platforms Portability to and scalability on new high-performance computers 15

16 Engaging Dakota Algorithms for Design Exploration and Uncertainty Quantification Website: Download (LGPL license, freely available worldwide) Getting Started guide User s Manual, Chapter 2: Tutorial with example input files Extensive documentation (user, reference, developer) Support mailing list (reaches both Dakota team and user community) At ASME V&V 2016 Dakota Team: Patty Hough Related authors/co-authors: Ken Hu, Sophia Lefantzi, Cosmin Safta, Greg Weirs, Walt Witkowski (and others who used Dakota in their ASME V&V 2016 work) Thanks for your attention! briadam@sandia.gov 16